It wasn't argue that God self-created or began to exist. I tried to denote I wasn't talking about a temporally initial set of properties, but a causally initial set: these aren't the same thing. It's still the case that it would be putting the cart before the horse to say God had any control over what God's properties were because no matter what point in eternity you check, it requires an already existing property of knowledge and power to do.
Also, that's a curious position; even most theists grant that omnipotence is still bounded by logical possibility. It isn't logically possible to even claim logical impossibilities, as a note.
He just is. There is no other way to express it.
Everything about God defies logic. Here is a single example.
2 Peter 3:8King James Version (KJV)
8 But, beloved, be not ignorant of this one thing, that one day is with the Lord as a thousand years, and a thousand years as one day.
1 day with the Lord is 1,000 years (with man)
This is not an exact mathematically formula. This is just used to convey the message that God pretty much exist outside of time. It is backed up by the Genesis example I gave you on other post about how 20 years in Eden was 20,000 or 30,000 years outside of Eden.
This defies all logic. It can kind of be explained with physics to some degree as Einsteins theory of relativity proves. If an object has a intense mass or gravity time will slow down. So one could say that God has a very large mass or strong gravity, not unlike a black hole, it could explain how time is slowed in the presence of the Lord. Although it does not explain everything like where is this mass etc. So it still defies logic.
I could go on all day but I don't have time for it. So I'll just leave it as God defies all logic, at the very least He defies our current understanding and logic. Maybe some day we will understand.